Question

What is the equation of the line that passes through the point (1,0) and is perpendicular to the line x+5y=30

Answer 1

Answer:

The equation of line passing through points (1 , 0) is  x - 5 y - 1 = 0    

Step-by-step explanation:

Given equation of line as

x + 5 y = 30

Now, equation of line in standard form is y = m x + c

where m is the slope

So,  x + 5 y = 30

Or, 5 y = - x + 30

Or, y = - $\frac{1}{5}$ x + 6

So, Slope of this line m = - $\frac{1}{5}$

Again , let the slope of other line passing through point (1 , 0) is M

And Both lines are perpendicular , So , products of line = - 1

i.e m × M = - 1

Or, M = - $\frac{1}{m}$

Or, M = - 1 × - $\frac{1}{\frac{1}{5}}$ =  $\frac{1}{5}$

So, equation of line with slope M and points (1, 0) is

y - $y_1$ = M × (x - $x_1$)

Or, y - ( 0 ) =  $\frac{1}{5}$ × ( x - 1 )

Or, y  =  $\frac{1}{5}$ x - $\frac{1}{5}$ × 1

Or, y  =   $\frac{1}{5}$ x - $\frac{1}{5}$

or, y + $\frac{1}{5}$ =   $\frac{1}{5}$ x

Or, 5×y + 1  =   x

∴ 5 y + 1 =  x

I.e  x - 5 y - 1 = 0

Hence The equation of line passing through points (1 , 0) is  x - 5 y - 1 = 0   Answer